Generalizing the Balance Heuristic Estimator in Multiple Importance Sampling
| Autor: | Mateu Sbert, Víctor Elvira |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Monte Carlo method Cross-entropy method Montecarlo Mètode de Monte Carlo importance sampling balance heuristic variance reduction chi-square divergence Kullback–Leibler divergence cross entropy General Physics and Astronomy Entropia creuada Mètode d' Estimació Teoria de l' Estimation Théorie de l' Statistics - Computation Computation (stat.CO) |
| Zdroj: | Entropy, 2022, vol. 24, núm. 2, p. 191 Articles publicats (D-IMA) DUGiDocs – Universitat de Girona instname Entropy; Volume 24; Issue 2; Pages: 191 |
| ISSN: | 1099-4300 |
| Popis: | In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable integrals. Then, we establish a generalized framework for the combination of samples simulated from multiple proposals. Our approach is based on considering as free parameters both the sampling rates and the combination coefficients, which are the same in the balance heuristics estimator. Thus our novel framework contains the balance heuristic as a particular case. We study the optimal choice of the free parameters in such a way that the variance of the resulting estimator is minimized. A theoretical variance study shows the optimal solution is always better than the balance heuristic estimator (except in degenerate cases where both are the same). We also give sufficient conditions on the parameter values for the new generalized estimator to be better than the balance heuristic estimator, and one necessary and sufficient condition related to χ2 divergence. Using five numerical examples, we first show the gap in the efficiency of both new and classical balance heuristic estimators, for equal sampling and for several state of the art sampling rates. Then, for these five examples, we find the variances for some notable selection of parameters showing that, for the important case of equal count of samples, our new estimator with an optimal selection of parameters outperforms the classical balance heuristic. Finally, new heuristics are introduced that exploit the theoretical findings. |
| Databáze: | OpenAIRE |
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